4,035 research outputs found
Spectral methods for CFD
One of the objectives of these notes is to provide a basic introduction to spectral methods with a particular emphasis on applications to computational fluid dynamics. Another objective is to summarize some of the most important developments in spectral methods in the last two years. The fundamentals of spectral methods for simple problems will be covered in depth, and the essential elements of several fluid dynamical applications will be sketched
Response of Bose gases in time-dependent optical superlattices
The dynamic response of ultracold Bose gases in one-dimensional optical
lattices and superlattices is investigated based on exact numerical time
evolutions in the framework of the Bose-Hubbard model. The system is excited by
a temporal amplitude modulation of the lattice potential, as it was done in
recent experiments. For regular lattice potentials, the dynamic signatures of
the superfluid to Mott-insulator transition are studied and the position and
the fine-structure of the resonances is explained by a linear response
analysis. Using direct simulations and the perturbative analysis it is shown
that in the presence of a two-colour superlattice the excitation spectrum
changes significantly when going from the homogeneous Mott-insulator the quasi
Bose-glass phase. A characteristic and experimentally accessible signature for
the quasi Bose-glass is the appearance of low-lying resonances and a
suppression of the dominant resonance of the Mott-insulator phase.Comment: 20 pages, 9 figures; added references and corrected typo
A fluctuating boundary integral method for Brownian suspensions
We present a fluctuating boundary integral method (FBIM) for overdamped
Brownian Dynamics (BD) of two-dimensional periodic suspensions of rigid
particles of complex shape immersed in a Stokes fluid. We develop a novel
approach for generating Brownian displacements that arise in response to the
thermal fluctuations in the fluid. Our approach relies on a first-kind boundary
integral formulation of a mobility problem in which a random surface velocity
is prescribed on the particle surface, with zero mean and covariance
proportional to the Green's function for Stokes flow (Stokeslet). This approach
yields an algorithm that scales linearly in the number of particles for both
deterministic and stochastic dynamics, handles particles of complex shape,
achieves high order of accuracy, and can be generalized to three dimensions and
other boundary conditions. We show that Brownian displacements generated by our
method obey the discrete fluctuation-dissipation balance relation (DFDB). Based
on a recently-developed Positively Split Ewald method [A. M. Fiore, F. Balboa
Usabiaga, A. Donev and J. W. Swan, J. Chem. Phys., 146, 124116, 2017],
near-field contributions to the Brownian displacements are efficiently
approximated by iterative methods in real space, while far-field contributions
are rapidly generated by fast Fourier-space methods based on fluctuating
hydrodynamics. FBIM provides the key ingredient for time integration of the
overdamped Langevin equations for Brownian suspensions of rigid particles. We
demonstrate that FBIM obeys DFDB by performing equilibrium BD simulations of
suspensions of starfish-shaped bodies using a random finite difference temporal
integrator.Comment: Submitted to J. Comp. Phy
IllinoisGRMHD: An Open-Source, User-Friendly GRMHD Code for Dynamical Spacetimes
In the extreme violence of merger and mass accretion, compact objects like
black holes and neutron stars are thought to launch some of the most luminous
outbursts of electromagnetic and gravitational wave energy in the Universe.
Modeling these systems realistically is a central problem in theoretical
astrophysics, but has proven extremely challenging, requiring the development
of numerical relativity codes that solve Einstein's equations for the
spacetime, coupled to the equations of general relativistic (ideal)
magnetohydrodynamics (GRMHD) for the magnetized fluids. Over the past decade,
the Illinois Numerical Relativity (ILNR) Group's dynamical spacetime GRMHD code
has proven itself as a robust and reliable tool for theoretical modeling of
such GRMHD phenomena. However, the code was written "by experts and for
experts" of the code, with a steep learning curve that would severely hinder
community adoption if it were open-sourced. Here we present IllinoisGRMHD,
which is an open-source, highly-extensible rewrite of the original
closed-source GRMHD code of the ILNR Group. Reducing the learning curve was the
primary focus of this rewrite, with the goal of facilitating community
involvement in the code's use and development, as well as the minimization of
human effort in generating new science. IllinoisGRMHD also saves computer time,
generating roundoff-precision identical output to the original code on
adaptive-mesh grids, but nearly twice as fast at scales of hundreds to
thousands of cores.Comment: 37 pages, 6 figures, single column. Matches published versio
Adaptive time-stepping for incompressible flow. Part II: Navier-Stokes equations
We outline a new class of robust and efficient methods for solving the Navier- Stokes equations. We describe a general solution strategy that has two basic building blocks: an implicit time integrator using a stabilized trapezoid rule with an explicit Adams-Bashforth method for error control, and a robust Krylov subspace solver for the spatially discretized system. We present numerical experiments illustrating the potential of our approach. © 2010 Society for Industrial and Applied Mathematics
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